Problem: $g(n) = -6n^{2}+6n+5-h(n)$ $h(t) = -3t^{2}+5t+6$ $f(x) = -4x^{3}-6x^{2}+7x-4(h(x))$ $ h(g(-1)) = {?} $
First, let's solve for the value of the inner function, $g(-1)$ . Then we'll know what to plug into the outer function. $g(-1) = -6(-1)^{2}+(6)(-1)+5-h(-1)$ To solve for the value of $g$ , we need to solve for the value of $h(-1)$ $h(-1) = -3(-1)^{2}+(5)(-1)+6$ $h(-1) = -2$ That means $g(-1) = -6(-1)^{2}+(6)(-1)+5-(-2)$ $g(-1) = -5$ Now we know that $g(-1) = -5$ . Let's solve for $h(g(-1))$ , which is $h(-5)$ $h(-5) = -3(-5)^{2}+(5)(-5)+6$ $h(-5) = -94$